Concepts: Calldown
Introduction
In this Article
- Requirements for calling with a made hand
- Formula for the EV of a calldown
- Guidelines for practical game
Notes:
- In this article, the term „made hand“ will refer to a hand with showdown value and just a few outs.
- Working with probabilities and expected values in poker often requires making good estimates about what has already been observed as well as a good understanding of people. For this reason, some values in this article are given as speculative values derived from experience or are simply assumptions made for argument's sake. Since these calculations are concerned with the order of the values and not the exact numbers, this speculation is justified.
A good player stands out because he is a TAG. That is, he has a moderate WentToSD value and a high aggression factor (Though these numbers on their own do not make a winning player. On the other hand, if they deviate too far from the optimum it is usually found that the player can only beat very weak opponents in the long run). A high aggression factor means that most actions are either folds (checks) or bets (raises). Calls should usually be avoided. From the beginner's section, it should be known that calls only make sense for a drawing hand when you have the necessary odds. Furthermore, since poker is a game of incomplete information situations can arise where one should call with a made hand, usually until the showdown, which is notable because it is there that the switch to complete information is made. It is these situations that we will examine more closely in this article. We will start with post-flop situations where the hero can (or must) choose between calling, raising, or folding.
Basic requirements for calling with a made hand
The basic principle of poker is to make the moves with the highest expected value. The expected values are calculated by considering the information available to each and every player. Since the EV of folding seems to be 0, it is always good to check whether calling or raising (as long as you aren't capped) has a positive EV. If you are probably leading with your made hand, raising is clearly (almost) automatically +EV. Depending on the situation and the folding tendencies of your opponents it is probably even worth it to raise with slightly worse showdown chances. With particularly good hands, the possibility of the slow play should be kept in mind. All of these cases are explicitly excluded from this discussion. Instead, we will examine the frequently made choice between calling or folding.
In the context of a made hand, the EV of a call depends on the probability (calculated from all available information) that one's own hand will be in the lead at the showdown, the cost of getting to the showdown, and the size of the pot at the showdown. Since we assume a made hand with showdown value, it's usually correct to call in later streets too after the first call is made since the cost to see the showdown falls while the size of the pot increases. A fold, then, is unthinkable unless a particularly bad card turns up that drastically reduces the value of your own hand or makes the betting action something special. Alternatively, a made hand could be improved by one of it's few outs, so that you would rather bet and raise in the later streets. Both cases are exceptions. For this reason, one will call or take a free card on the later streets in 80% of cases where one has already called once with a made hand. There is also the calldown. If the EV of a call with made hand is nearly the same as the EV of a calldown (the EV of a call is at least as high as a calldown, since with a calldown there is a small, but finite, probability of making a less than optimum call somewhere in the later streets). The following formula is valid for the EV of a calldown:
EV(calldown)= -EV(cost of showdown)+ EV(pot at showdown)*EV(share of pot at showdown)
where EV(cost of showdown) refers to the big bets we'll have to pay to see the showdown,
EV(pot at showdown) is the EV of the number of big bets in the bot at showdown and EV(share of pot at showdown), also called equity, is the probability that we will win moderated by the possibility of having to share the pot.
Now if
EV(share of pot at showdown) > EV(cost of showdown)/EV(Pot at Showdown)
and a raise is not reasonable, one should call the hand.
Parameters in the formula for the EV of a Calldown
To use the formula above, we must quantify the above parameters a little more rigorously:
· EV(cost of showdown): The cost of the showdown consists of the count of the bets which must be immediately called and, if used, the bets one would have to make if one were raised from behind and when betting occurs in the later streets. It follows that this value can only be determined exactly for the player who takes the final turn on the river. It's also fairly easy to estimate with two players. On the flop it's usually around 2.1 BB (a sure .5 on the flop, an average of .9 on the turn and ca. .7 BB on the river). It's lower on the turn at about 1.7 BB (at least 1 BB on the turn, an average of .7 on the river). These estimates can be refined with the proper reading of the opponents. It's more difficult to express this EV in multiway pots, but a good gut will be able to tell it's value relative to a single pot. This excludes the case where there is an aggressor (or there will be on later streets) or the case where multiple players begin to whet their blades. The latter gives rise to raising wars which can lead to an explosion in the cost for the showdown, since there are now not just 1 BB per street but 3 or 4. Thus, the fifth most important factor for the EV(cost of showdown) are the indicators of a coming raising war. These include the previous betting patterns, the board, the number and aggression of the players in the hand, and your own position. The betting patterns thus far give some indication of the number of aggressors and the probability that more than one person hit a good hand and would play it aggressively. On dangerous Boards there is increased danger that more than one player will hit a monster. The more players, the more potential betters and raisers there are. Aggressive players, of course, tend to raise and bet often. Combinations of maniacs are particularly dangerous (maniac v. TAG or maniac v. Maniac). TAG v. TAG carries a smaller risk, since TAGs will respect the expression of power by the opposition. Finally, position is important; for example, this determines whether someone can raise behind you. Sitting between two aggressors, it's easy to become trapped as a raising mule.
· EV(Pot at Showdown): This EV consists of the current pot and the expected payments therein by the remaining players. In heads-up situations, the formula is
EV(Pot at Showdown) = Pot + 2*EV(cost of showdown) – X,
where X=.5 on the flop and X=1 on the turn/river (X is the bet of the aggressors that must be called). In multiway pots the calculation is more complicated, since one must reckon with the number of players left in the later streets. It can be estimated with
EV(pot at showdown)=Pot+((N+M)/2)*EV(cost of showdown)-n*X,
where N is the current number of players, M is the estimated count of players at showdown and n is the number of players who have already called. There is so much variance in the guesses for this formula that it's almost best just go on instinct when estimating the EV(pot at showdown).
· EV(share of pot at showdown): The lesson of this parameter is hand reading. This theme has been introduced in previous articles. This skill is very important to making calldown decisions. One should always think in ranges of hands. In this way, one can decide what percent of hands will result in a loss and what percent a win. Examples of ranges are: Same pair Lower Kicker, any monster, bluffs, and so on. Depending on the looseness and aggressiveness of the opponents and the previous betting patterns, individual hand ranges can be assigned a probability. The result of such an analysis might be something like: bluff 15%, lower/underpair 10%, same pair lower kicker 25%, same pair higher kicker 15%, overpair 10%, high cards 25%. In that case one would have a 25% probability with a top pair and mediocre kicker. Since the EV(share of pot at showdown) always refers to the showdown, the draw chances (mostly for yourself, since one is always behind!) must also be estimated. Depending on the danger of the board, your own outs and the behaviour of your opponents, the equity value lies a little higher than the probability that one is currently leading. As mentioned in the beginning, a calldown should only be considered if the equity is smaller than 1/N where N is the number of players in the hand.
In multiway pots the equity in calldown situations is often less than desirable, since if 3 (or even 4 or 5) players haven't folded by the showdown, it will come to the so-called river overcalls. In this case if the probability to beat another hand is p, you will win in only about p/2 of all cases since you must beat all other opponents as well. Their payments into the pot do not overcome this problem.
Guidelines for the practical game
We have answered the question of the correctness of a calldown from a formal perspective. With a little practice, you'll be able to do the formulas in your head. However, these general calculations allow us to make a simple derivation from simple ground rules.
1. Only call down if you are probably (but not surely) behind.
(As was mentioned before, one should play aggressively with an equity advantage to squeeze the value out of it. If one has surely lost, folding is the only option.
2. Call down in big pots and fold if the pot is small
(EV(cost of showdown) is small in relation to EV(pot at showdown) when the pot is large, so EV(share of pot at showdown) doesn't have to be so high.)
3. Increase your willingness to calldown on later streets
(the longer the way to showdown, the larger the EV(cost of showdown) and so better equity is needed)
4. Avoid calldowns in a multiway pot. Especially fold if there is the danger of a raising war
(While it's true that multiway pots are often quite large, they are usually unprofitable for the reasons listed above as well as for equity.)
5. Estimate your chances to win the hand using all available information. Think in hand ranges.
(The profitability of a calldown is heavily dependent on the probability of being in the lead)
Psychology Guide
Weak tight players think calldowns are leaks and that one usually loses from them. They would fold instead. They feel vindicated because of their selective perception. This approach is wrong. As we've seen and like so much of poker, it's all about the EV. Many calldowns are so profitable that it will do to win every third or fourth one. One should keep that in mind when gnashing teeth about, as feared, handing over the pot to the coffers of one's opponent.
An example from Ed Miller illustrates this point. Suppose we're playing on FishyPoker.com and there is a special promotion of $10 mil added to the pot. How should we play? Calldown (here value raise) of course! It is exactly the same with any pot that is big enough in relation to our equity.
Example Hands
Here are some example hands:
We have A
Q
in the CO of a full ring game.
Preflop: MP1 calls before us and all others fold. We raise, the buttons and the blinds fold. MP1 calls again.
Flop: 7
Q 3 . We bet and the villain calls
Turn: A makes the board a 4-flush. The pot has 4.75 BB. What should we do? It depends on the opponent.
Calling Station: This bet is disquieting. Given the passivity of our opponent it is usually a sign of power. A bluff is only 5% likely. There could also be an overestimation of the board. The calling station is 15% likely to have an Ax and in 3% of cases will have a slowly played set. We also have a 9% chance of getting a full house on the river. This means we can expect to win the hand 35% of the time. We have only two options: calldown or fold. The expected cost of the showdown is somewhere around 1.5 BB (1 BB now and 50% likely 1 more BB on the river; a passive player would often have a little flush or a combination that we could not beat and still not bet on the river). Consequentially, we calculate a total pot at 4.75+2*1.5-1= 6.5. Since .35>1.5/6.25 a calldown is profitable here.
Maniac (extreme): This bet is unimpressive, since a maniac would bluff bet 80% of the time even without a flush. We can assume that his suits are random, in ca. 50% of all cases a flush (just by calculating on the assumption of a random deal,
1-(3/4)^2=43.75%). He surely does not have a set, since he would have raised all pocket pairs on the pre-flop. Hence, we have a marginal advantage of equity and can raise. If we only get called, it almost certainly indicates that he doesn't have a flush. We can then bet again on the river. If the maniac caps on the turn, we have to rethink our position. He could now have a flush 60% of the time. That means we no longer have an advantage in equity (and nearly no fold equity!), but a calldown is profitable in any case, especially considering the size of the pot.
Rock: It is the timid rock who is very careful about such bets. 95% of the time this indicates a flush, and we don't anything like a made hand. We can only win the pot if we hit a full house. For this purpose we have four almost-clean outs, so our total equity is around 17%. It is clear that the pot is not big enough to justify a call.
TAG: It would be most uncommon for a TAG to play a hand that way.
We're playing a typical loose SH game with a lot of fish (loose-neutral, VP$IP 40-50%, PFR 10%, AggrPF 1-1.5, play somewhat trickily with a tendency to make senseless opportunistic bluffs and remarkable moves).
Preflop: In the second position we get J J. The UTG limps, we raise, CO folds and the button makes a coldcall. The SB folds. BB and UTG are increasing the stakes, in any case.
Variant 1:
Flop: Q 2
7 . The UTG checks, we bet, button re-raises, BB folds and UTG 3-bets. The pot is now at 6.75 BB. Should we fold, call, or raise?
Since there are only two outs that would better our hand, their draw value is rather smaller. We would be on the bare edge of recovery if someone had but a single Q. The same is good for sets and two pairs. Since 2 and 7 are low cards, the probability of middle/bottom pairs is small despite the high VP$IP value. So we are at most with 10% probability in the lead, and we are faced with ruination if an A or K shows up on the turn or river. Since a raising war would really grind us up, the showdown costs will be high with respect to our share in the pot. The hand is a clear fold.
Variant 2:
Flop: Q 2 7 . The UTG checks, we bet, button calls, BB folds and UTG calls.
Turn: 9 . UTG checks, we bet and BB raises. UTG folds. The pot now has 9.75 BB. How should we play if we know that the button is a limit-typical fish?
As in the first variant, our hand hardly has and potential for improvement. It's between a value raise, calldown, or a fold. Since the button is playing somewhat guilefully and partially even irrationally, there are three possible scenarios: the villain has a strong hand and has played it slow. He improved with the turn (probably to two pair), or he's bluffing. Since we have shown strength on all streets so far, the probability of this fortuitous bluff is about 15%. The probability of winning the pot is somewhere around 17%, since we could improve by way of our two outs (the outs of the button are less relevant, since he will already be ahead 85% of the time). Since a raise for free showdown will not work against a strong hand and a value raise is out of the question, a raise here would be a mistake. The cost of the showdown is somewhere in the neighbourhood of 1.8BB per round. The pot at showdown would then be on average 9.75+2*1.8-1=12.35
EV(share of pot at showdown) = 0.17 > 0.14...=1.8/12.35 =EV(price for showdown)/EV(pot at showdown)
So the pot is fat enough to stay in the hand. The decision is close, however, and could be reversed depending upon the assumptions about probability.
Variant 3:
Flop: Q 2 7. The UTG checks, we bet, button calls, BB folds and UTG calls.
Turn: 9 . UTG checks, we bet, BB calls and UTG calls.
River: 9 . UTG checks, we bet, BB raises, UTG folds. Should we go to the showdown with button over a pot of 11.75+1=12 BB (button is a typical fish)?
We were probably rivered or caught in a slowplay trick. In any case is would be a catastrophe to give away this pot if it's rightfully ours. And there are always hands we can beat, particularly bluff hands. Our chances to win the pot are surely greater than 8%. Therefore, a call is profitable.
We're on the button in a loose-passive full ring game holding 8 9 . We just jumped in on the round before so we don't have any definite reads on the individual players.
Preflop: Thanks to four limpers (UTG, MP1, MP2, CO) before us, we have great odds. We call too. SB finishes and BB checks.
Flop: 6 5 7 .The flop is both curse and blessing. The blinds check, UTG checks, MP1 bets and MP2 calls. CO folds. We raise our straight. After the fold of the SB and the coldcall of the BB comes a fold from UTG, and a 3-bet from MP1. MP2 folds and we have to decide whether our hand is strong enough to fight with the four remaining players over a 7.5 BB pot.
Since we have a nut straight, it's presumable that we are only threatened with a flush. It's not unlikely, given the seven players at the table. But we will lose for sure if another heart shows up. Before the river this will happen with a probability of 35%. The probability that someone already has a flush can be estimated at 60%, since fish love to play suited hands and even a random distribution amongst 7 people would produce this flush about 50% of the time. The events are not disjoint, however, since the probability that no fourth flush card comes before the showdown and that nobody holds two hearts is smaller than 85%. We can guess that it's around 75%. This value must be corrected upward because MP1's actions imply that he could have a strong hand. Because of passivity our opponent is probably a flush. A loose-passive fish would only value bet on a strong draw as an exception, and a pure bluff is very unlikely. Thus, the assumption that we will win in 15% of cases is fairly realistic. For reasons of computation let us take it to be 20%, since we will fold at the first sign of a fourth flush card, thereby avoiding wasting bets. Thus, the EV of a call is higher than the EV of a calldown, so this computational assumption will balance that effect. The expected costs of the showdown are very high in this case, since we're only on the third street and we can count on paying probably 2 and more bets. We can speculate that the showdown will cost us 4BB and the pot will be worth 20 BB. Therefore, we fold.
Conclusion
The examples have shown that the profitability formulas for a calldown can ease the decision and execution of them. Of course it is hardly possible, especially if one is playing multiple tables, to perform a precise EV calculation. A quick estimate will suffice. Additionally, it's also useful for analysing one's own game. If you examine a few questionable hands with the help of the formulas after a session, you'll quickly get a feel for when a calldown is +EV.
Finally, I would like to point out that a missed calldown can induce your opponent to bluff more in the future. Hence he will exploit a leak without mercy and send your winning rate plunging. This should not cause one to play too loosely. A too-tight game is also a mistake, even if it's not as extreme as too loose.
Additionally, I would like to recommend this article post by Ed Miller in the 2+2 forum.